Add to ORKGAbstract We prove that random groups in the Gromov density model, at any density, satisfy property (FA), i.e. they do not act non-trivially on simplicial trees. This implies that their Gromov boundaries, defined at density less than 12, are Menger curves. Mathematics Subject Classification (2000) 20F65 · 20F67 · 20E08
This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary...
11 pagesWe work in the density model of random groups. We prove that they satisfy an isoperimetric i...
We show that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set ...
We study Property (T) in the $\Gamma(n,k,d)$ model of random groups: as $k$ tends to infinity this g...
For random groups in the Gromov density model at d<3/14, we construct walls in the Cayley complex X ...
36 pagesInternational audienceDeveloping an idea of M. Gromov, we study the intersection formula for...
We prove a Banach version of Żuk’s criterion for groups acting on partite (i.e., colorable) simplici...
The standard (n, k, d) model of random groups is a model where the relators are chosen randomly from...
Abstract. We consider models of random groups in which the typical group is of intermediate rank (in...
International audienceWe consider models of random groups in which the typical group is of intermedi...
We consider a family of random trees satisfying a Markov branching property. Roughly, this property ...
Abstract. We give a lower and an upper bound for the conformal dimension of the boundaries of certai...
Magnus' Freiheitssatz states that if a group is defined by a presentation with $m$ generators and a ...
International audienceWe prove that random groups at density less than 1/6 act freely and cocompactl...
We prove that a random group in the triangular density model has, for density larger than 1/3, fixed...
This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary...
11 pagesWe work in the density model of random groups. We prove that they satisfy an isoperimetric i...
We show that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set ...
We study Property (T) in the $\Gamma(n,k,d)$ model of random groups: as $k$ tends to infinity this g...
For random groups in the Gromov density model at d<3/14, we construct walls in the Cayley complex X ...
36 pagesInternational audienceDeveloping an idea of M. Gromov, we study the intersection formula for...
We prove a Banach version of Żuk’s criterion for groups acting on partite (i.e., colorable) simplici...
The standard (n, k, d) model of random groups is a model where the relators are chosen randomly from...
Abstract. We consider models of random groups in which the typical group is of intermediate rank (in...
International audienceWe consider models of random groups in which the typical group is of intermedi...
We consider a family of random trees satisfying a Markov branching property. Roughly, this property ...
Abstract. We give a lower and an upper bound for the conformal dimension of the boundaries of certai...
Magnus' Freiheitssatz states that if a group is defined by a presentation with $m$ generators and a ...
International audienceWe prove that random groups at density less than 1/6 act freely and cocompactl...
We prove that a random group in the triangular density model has, for density larger than 1/3, fixed...
This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary...
11 pagesWe work in the density model of random groups. We prove that they satisfy an isoperimetric i...
We show that the uniform unlabelled unrooted tree with n vertices and vertex degrees in a fixed set ...